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We introduce a higher dimensional quasiregular map analogous to thetrigonometric functions and we use the dynamics of this map to define, for d>1,a partition of d-dimensional Euclidean space into curves tending to infinitysuch that two curves may intersect only in their endpoints and such that theunion of the curves without their endpoints has Hausdorff dimension one.

Dynamics of a higher dimensional analog of the trigonometric functions